NTNU Norwegian University of Science and Technology Faculty of Information Technology and Electrical Engineering Department of Electric Power Engineering
Master ’s thesis
Jens Fredrik Lunde
Electric field distribution in layered polymeric HVDC insulation
Master’s thesis in Energy and the Environment Supervisor: Frank Mauseth
July 2020
Jens Fredrik Lunde
Electric field distribution in layered polymeric HVDC insulation
Master’s thesis in Energy and the Environment Supervisor: Frank Mauseth
July 2020
Norwegian University of Science and Technology
Faculty of Information Technology and Electrical Engineering Department of Electric Power Engineering
Preface
This project is the result of a graduating master thesis performed at NTNU during spring 2020. This particular project is performed at the Department of Electric Power Engineering in cooperation with SINTEF Energy Research (LowEmission Research Centre).
Due to the outbreak of the COVID-19 virus, the project has undergone some revisions throughout the semester as a nation-wide quarantine would not al- low work in the laboratory for parts of the semester. Theoretical calculations are therefore used as a supplement to the measurements that were performed.
I would like to thank my supervisor Frank Mauseth and my co-supervisor Øystein Hestad for their guidance and assistance during the project, even though the project did not turn out as planned. I would also like to thank Hans Helmer Sæternes, Jorunn Hølto and Torbjørn Ve at SINTEF for their assistance in the sample making process, with the DSC measurements and with the the laboratory measurements and data analysis, respectively.
Trondheim, July 9, 2020 Jens Fredrik Lunde
Abstract
The HVDC power transfer scheme has become more prevalent in recent times as it is the preferred scheme for long range power transfer. As the cable is stressed based on local fluctuations such as ambient temperature and field enhancements, the need for a greater understanding of the underly- ing mechanisms affecting the cable becomes more emphasized. Flat, layered samples are used for measurements as they can be used to emulate cable joints/terminations which are considered weak points of a cable.
This project will investigate the space charge accumulation and resulting field enhancement of layered polymeric HVDC insulation. The samples are comprised of two layers of cross-linked polyethylene (XLPE) where one layer is cross-linked once while the other is cross-linked twice. This is to create a discontinuity of the conductivity between the layers which should facil- itate charge trapping. The measurements are performed using the Pulsed Electro-Acoustic method (PEA) with an applied voltage of 10 kV and with temperatures of 20, 40 & 60°C. Finally, the viability of using an equivalent RC circuit as a prediction of the field development has been investigated.
The results show that the greatest charge accumulation occurs at 40°C, while the amount of accumulated charges are quite similar at 20 & 60°C. Hete- rocharges was observed at the cathode for all samples, while homocharges was present at the anode for all samples. At the dielectric interface charges of negative polarity was observed at all temperatures, but more positive charges was observable with higher temperatures. The heterocharges at the cathode lead to a field reduction in the range of 9.1-47.4% while the homocharges at the anode lead to a field enhancement in the range of 6.7-40.4%.
While the system is quite complex and many mechanisms are influencing the results at the same time, a possible reason for the observed results is that the space charge formation increases slower with increasing temperature than the charge detrapping in the samples, possibly as a result of the increasing mobility of the charge carriers. Other influential mechanisms may be the electrode materials, sample morphology, charge transport in the sample and charge injection.
Representing the samples in terms of an RC circuit was discovered to be viable at low temperatures as fewer mechanisms were present. At higher temperatures more mechanisms were observed and the accuracy of the model decreased. More RC branches could be added in order to rectify this, however at the cost of making the model significantly more complex.
Sammendrag
HVDC overføring har blitt mer og mer vanlig ettersom det er foretrukket over HVAC overføring over lengre distanser. Siden kabelen erfarer ulik p˚akjenning basert p˚a lokale variasjoner innen blant annet temperatur og felt er det nyttig
˚a utføre dybdeundersøker p˚a hvordan disse mekanismene kan p˚avirke kab- lene. Flate, lagdelte prøver brukes under m˚alingene siden de kan etterligne kabelskjøter/termineringer som anses ˚a være et svakt punkt p˚a en kabel.
Det er derfor denne masteroppgaven undersøker hvordan romladningsopp- samling og resulterende feltutvikling p˚avirker lagdelt polymerisk HVDC iso- lasjon. Prøvene best˚ar av to lag kryssbudet polyetylen (PEX) hvor det ene laget er kryssbundet ´en gang, mens det andre er kryssbudet to ganger. Dette er gjort for ˚a danne en diskontinuitet i konduktiviteten mellom lagene for ˚a framprovosere ladningsoppsamling. M˚alingene er utført ved ˚a bruke Pulsed Electro-Acoustic method (PEA) med en p˚aført spenning p˚a 10 kV over prøven og med temperaturer p˚a 20, 40 & 60°C. Til slutt er muligheten for ˚a bruke en ekvivalent RC model som en prediksjon av feltutviklingen vurdert.
Resultatene viser at den største ladningsoppbyggingen forekommer ved 40°C, mens mengden av oppsamlede ladninger ved 20 & 60°C er ganske like. Het- eroladninger er observert ved katoden i alle prøver, mens homoladninger forekommer ved anoden i alle prøver. Ved den interne grenseflaten observeres negative ladninger ved alle temperaturer, men mer positive ladninger ob- serveres ved høyere temperaturer. Heteroladningene ved katoden fører til en feltreduksjon mellom 9.1 og 47.4%, mens homoladningene ved anoden fører til en feltøkning mellom 6.7 og 40.4%.
Selv om systemet er svært komplekst og mange mekanismer p˚avirker resul- tatene samtidig er likevel en mulig forklaring p˚a de observerte resultatene at romladningsformasjonen øker saktere ved økende temperatur enn ladnings- frigjøringen. Dette kan komme av økende mobilitet i ladningsbærere ved økende temperatur. Andre p˚avirkende mekanismer kan være elektrodemate- rialet, prøvens morfologi, ladningstransport i prøven og ladningsinjeksjon.
˚A representere prøvene i form av en RC krets viste seg ˚a være mulig p˚a lavere teperaturer siden færre mekanismer er tilstede. Ved høyere temperaturer kan flere mekanismer observeres og nøyaktigheten til modellen synker. For ˚a forbedre dette kan flere RC grener legges til, men dette fører til at modellen blir betydelig mer kompleks.
Contents
1 Introduction 1
2 Theory 2
2.1 Dielectric properties of a material . . . 2
2.2 Conductivity . . . 3
2.3 Space charges and electrical fields . . . 4
2.3.1 Classification of space charges . . . 5
2.3.1.1 Homocharges . . . 5
2.3.1.2 Heterocharges . . . 6
2.3.2 Polarisation . . . 6
2.4 Charge injection . . . 8
2.4.1 Band theory applied to polymers . . . 8
2.4.2 Ionic conduction . . . 9
2.4.3 Electronic conduction . . . 9
2.4.4 Schottky- and Fowler-Nordheim injection . . . 10
2.5 Detection of space charges . . . 11
2.5.1 Attenuation and dispersion . . . 12
2.5.2 Calibration . . . 14
3 Method 15 3.1 Layered test objects . . . 15
3.1.1 Degassing . . . 16
3.1.2 Sputtering . . . 16
3.2 Experimental setup . . . 17
3.2.1 Conditioning . . . 18
3.2.2 Calibration . . . 18
3.3 RC-equivalent circuit . . . 18
4 Results 21 4.1 Layered test objects . . . 21
4.1.1 L1 - 20 kV/mm - 20°C . . . 21
4.1.2 L2 - 20 kV/mm - 40°C . . . 25
4.1.3 L3 - 20 kV/mm - 60°C . . . 28
4.2 The temperature effect . . . 31
4.3 RC-equivalent . . . 33
5 Discussion 34 5.1 Charge development . . . 34
5.2 Field development . . . 37
5.3 RC-equivalent . . . 37
6 Conclusion 39
7 Further work 40
A Appendix 44
A.1 Conductivities and RC-components . . . 44 A.2 DSC measurements . . . 45
1 Introduction
With an increased focus on long range power transfer comes an increased interest in the HVDC power scheme due to the significant advantages this scheme presents compared to the HVAC scheme. Although HVDC substa- tions are more costly than HVAC substations, advantages such as lower losses at equal conductor current, lower cable cost for equal power transfer due to reduced amount of conductors and the non-necessity for reactive power compensation makes HVDC the preferred scheme for long range power trans- fer [1] [2, Ch.14].
When DC voltage is continuously applied to a system, an inherent trapping of space charges occur in the insulation. These charges affect the local field of the insulation which could be problematic in case of a short circuit or voltage polarity change. The discharge of the trapped charges depend upon the depth of the trap, meaning the charges can remain in the insulation for long periods of time even if no voltage is applied.
Due to the aforementioned reasons, it is of interest to further investigate the mechanisms of space charge accumulation in HVDC cable systems. In this project, samples of the HVDC material cross-linked polyethylene (XLPE) is used. Depending upon the load of the cable as well as the ambient tem- perature of the surrounding environment, different conditions may apply to different parts of a cable, meaning different rates of space charge accumu- lation may occur. The effect of temperature on the accumulation of space charges is therefore investigated further in this project.
The samples are layered, where one of the layers is cross-linked once, while the other is cross-linked twice. This is to create an internal interface in the sample to mimic a cable joint, which is considered a weak point of a cable.
This master project has a related preceding specialization project where the effects of applied voltage as well as the internal interface were studied. An increase in the accumulation of space charges was found to correlate with an increase in the applied field, but an insufficient amount of different voltage levels were applied in order to make any trends. Few conclusions were able to be drawn with regards to the internal interface, however theory emphasizes the difference in two materials’ conductivity and permittivity as the main factors for space charge build-up at a dielectric interface.
2 Theory
Before the introduction of the experiments and the following analysis of the results, it may be useful to present theory which serves as the basis for the experiments. This chapter will review relevant theory which is used when discussing the acquired results. Note that most of the theory was previously presented in the specialization project preceding this master’s thesis, and only minor additions or corrections have been made to the section [3].
2.1 Dielectric properties of a material
A perfect dielectric material may be defined as a material which has no transport of charge carriers, meaning electrons, holes or ions, as well as a permittivity which is independent of frequency and temperature [4]. How- ever, in reality the perfect insulator does not exist which means there will always be some charge carrier transportation through the insulation. Poly- mer is a popular choice as an insulation medium and will be the focus of this project, so it will be used for further explanation of dielectricity [4].
In the 90s there was a large ongoing operation from cable manufacturers to phase out the common oil-paper insulated cables in favor of extruded cable insulation. This led to the expansion of the polymer-based cable insulation, usually based on polyethylene. The extruded cables had some advantages compared to traditional oil-paper cable insulation, like [1, 5]:
• Higher conductor temperatures, giving a more compact cable at the same power rating
• A lighter cable due to lighter moisture barriers
• Easier process when adding joints
• No pollution related to oil-leaks
• Lower cost
When making an extruded cable you may either use pure materials or ma- terials with additives to improve certain properties of the cable insulation.
The pure insulation typically suffer from undesirable properties such as high space charge accumulation or a high temperature dependence with regards to its breakdown voltage, leading to an abandonment of this type of insulation in favor of insulation containing proper additives [1].
The additives in polymeric cable insulation may be divided into several cat- egories depending on their function. These categories are [6]:
• Auxiliaries, which generally include catalysts used in crosslinking and as emulsifying agents. Some of these may only be used during the manufacturing process and only have remaining residues while others remain in the insulation after the manufacturing process.
• Additives, which are added in small concentrations, generally less than 10%, and does not substantially alter the structure of the polymer but changes some of its properties. The additives may include lubricants and parting agents to improve flow characteristics, stabilizers for heat- and ultraviolet-protection, antioxidants to prevent oxidation, flexibiliz- ers to improve toughness, etc.
• Compounding ingredients are added in large concentrations, typically 10-70%. They are divided into two sub-groups: fillers and plasticis- ers. Fillers are used to reduce the cost of the insulation while also improving some of its mechanical properties and electrical insulation characteristics. Plasticisers are generally used to reduce the brittleness of the insulation.
Using proper additives may lead to the insulation having outstanding electric properties such as the ones listed in table 2.1:
Table 2.1: Typical electric properties of XLPE cable insulation [4]
XLPE Dielectric loss factor, tan(δ) 1.5·10−4
Insulation resistivity, ρ 1019 Ω cm (Theoretical) Breakdown strength, Eg 500 kV/mm
Comparing this to older mass-impregnated cables which could have an im- pulse breakdown strength of 110mmkV and a resistivity of ≈ 1014Ωcm, the advantageous properties of XLPE cable insulation are highlighted [7].
2.2 Conductivity
The conductivity of any given material may be defined as the transport of charge carriers through a medium, that being either electrons, holes or ions. When applying a DC field, the charge transport is dependent on the conductivity σ and can be expressed by [8]:
J =σE (2.1)
whereJ is the current density. For a polymer the conduction mechanisms are rather complex because of its semi-crystalline nature [7]. Generally, the con- ductivity σ varies exponentially with the temperature and can be expressed as:
σ=σ0exp(− φ
kT) =X
qiniµi (2.2)
whereσ0is a material constant,φis the activation energy,k is the Boltzmann constant, T is the temperature, qi, ni and µi is the charge, density and the mobility of the i’th carrier, respectively. This shows how many factors play a part in the determination of the conductivity of the material, meaning it might depend upon the samples preparation and thermal history, making it difficult to determine the conduction mechanism [7].
2.3 Space charges and electrical fields
When applying a voltage over a material, an electric field arises. For homo- geneous, flat materials the electric field can be expressed as:
E = U
d (2.3)
where U is the applied voltage and d is the width of the material.
With an applied AC voltage, the above expression is sufficient to represent the electrical field, but in DC conditions the applied voltage is constantly of the same polarity and amplitude. Charge carriers in the insulation may then be trapped in the material, creating space charges. Space charges are a discrepancy in the amount of charges going in and out of an area and is an unwanted property. The accumulation of space charges are increased at the electrode-polymer interface as well as internal interfaces of the insulation, meaning the condition of the interfaces are crucial factors. In the bulk of the insulation, space charges may arise due to ionisation of impurities [7]. The space charges increase the local field and if the charge density is sufficiently high, the electrical field may exceed the breakdown strength of the material, leading to failure [1]. The DC electrical field may now be expressed as [9]:
E~DC =E~AC+E~ρ (2.4)
where E~ρ is the additional field due to the accumulated space charges.
The space charge density ρ can be expressed as [4]:
ρ=div ~D (2.5)
where D~ is the electrical flux density. It can further be defined as:
D~ =εrε0E~ (2.6)
whereεr is the relative permittivity of the material andε0 is the permittivity in vacuum. Combining equation 2.5 and 2.6 gives:
ρ=∇(εrε0E~ρ) (2.7)
Recognizing that
E~ =−∇φn (2.8)
where φn is the potential at point n, gives Poisson’s equation, expressed by:
∇2φ=− ρ
εrε0 (2.9)
which might also be useful when calculating the field.
The field enhancement factor FE% is typically used to describe the local enhancement in the electric field caused by the accumulated space charges.
The factor is a percentage value of the increase or decrease in the field, where for flat objects it is represented as [9]:
FE% = Emax− Ud0
U0
d
100 (2.10)
2.3.1 Classification of space charges
The accumulated space charges are usually expressed differently according to the polarity of the space charge in regard to its adjacent electrode. Space charges with equal polarity to that of the adjacent electrode are regarded as homocharges while those with opposite polarity are regarded as heterocharges [7]. A brief description of the two classifications and their significance follows.
2.3.1.1 Homocharges
When the charge has the same polarity as the adjacent electrode it is called ahomocharge. Effectively, this means that the dielectric is unable to conduct the charges faster than they are injected, leading to the accumulation of equal polarity charges at the electrode [1,10]. This leads to a decreased field at the interfaces, but a higher field in the bulk of the insulation, presented in figure 2.1a.
(a)
(b)
Figure 2.1: (a) Electrical field distribution of electrode gap under influence of homocharges where E0 = Vd0 and (b) is a representation of homocharges in terms of the charges at the electrodes [1].
2.3.1.2 Heterocharges
Heterocharges occur when the polarity of the charge is of the opposite po- larity of the adjacent electrode. This means that the interfaces are unable to convey the charges at the same rate as the dielectric is able to conduct them. The electrons and positive charges migrate towards the electrode of opposite polarity and is trapped at the interface. This leads to an increase in the electric field at the interfaces of the dielectric [1].
(a)
(b)
Figure 2.2: (a) Electrical field distribution of electrode gap under influence of heterocharges whereE0 = Vd0 and(b)is a representation of heterocharges in terms of the charges at the electrodes [1].
2.3.2 Polarisation
Polarisation is a temporary alignment of dipoles in the dielectric caused by an externally applied electrical field which causes a change in the flux den- sity, varying with time. The polarisation may either vanish instantly after
the field is removed, a so-called momentary polarisation, or it may grad- ually decrease with an exponential time constant τ, known as a relaxation mechanism. Following are short descriptions of the four different polarisation mechanisms which may be present in a dielectric [4].
Electronic polarisation
When an electric field is applied to a dielectric, the individual atoms are affected. As the electrons are orbiting the nucleus, the negatively charged electrons tends to drift closer to the positive electrode under the effect of the electric field while the positively charged nucleus tends to drift towards the negatively charged electrode. This creates a temporary induced dipole proportional to the electric field. This effect is temporary and is considered a momentary polarisation [4].
Ionic polarisation
Materials comprised of ionic bonded atoms have no inherent dipoles. How- ever, when placed in an electric field, the positively charged ions drifts to- wards the negative electrode, while the negatively charged ions drifts towards the positive electrode, creating a lattice distortion. This induces a tempo- rary dipole in the material which vanishes when the field is removed. This is therefore considered as a momentary polarisation [4].
Orientational polarisation
Some substances comprised of permanent dipoles such as water have no in- herent polarisation under normal circumstances, due to the molecules having a non-symmetrical arrangement. Under the influence of an electric field the dipoles may line up, creating a polarisation. The orientational polarisation1 can be considered proportional to the electric field, while also inversely pro- portional to the absolute temperature for gaseous or liquid substances, while in solids the relationships between the polarisation, electric field and tem- perature are more difficult to determine. After removal of the field, the dipoles will slowly descend back into disorder, meaning this is a relaxation mechanism [4].
Interfacial polarisation
At any section of a dielectric where there is an interface between two dif- fering materials and an electric field is applied, charge build-up may occur due to differing values for the permittivity and conductivity of the two ma- terials. This effect is also known as the Maxwell-Wagner-Sillars effect. The phenomenon may also be caused by additives in the dielectric such as fillers
1Also known as the dipole- or molecular polarisation
or impurities in the bulk of the material. This mechanism is only relevant for external electric field at sufficiently low frequencies as the movement of charges are not able to follow the changing polarity for higher frequencies.
This is considered as a relaxation mechanism [4, 11] [12, Ch.5].
2.4 Charge injection
The concept of charge injection and transport in polymers may be defined in two different ways; ionic- and electronic conduction. For any given material the relevant charge carrier is dependent on several internal- and external factors such as: the materials chemical- and physical composition, frequency of the applied field and temperature, among others [6].
2.4.1 Band theory applied to polymers
A useful way of explaining band theory when considering polymers is to apply Niels Bohrs model of atoms. It states that electrons are only allowed certain discrete energy levels corresponding to different orbitals in the model. The material may either absorb energy, exciting electrons to higher energy levels, or emitting energy leading an electron to ”drop” energy levels. The high- est filled energy band during absolute zero conditions is called the valence band, while the first unoccupied band is called the conduction band. Be- tween the two bands is the band gap, sometimes known as theforbidden band gap2. The size of the band gap determines the materials ability to conduct electricity, exemplified by insulators having a band gap greater than 2 eV3, semi-conductors being in the region of 0.2-2 eV and conductors less than 0.2 eV [6].
Impurities in the polymer gives rise to incompletely-bound atoms which in turn creates so-called dangling bonds, which can be satisfied by adding or removing an electron (or both), effectively allowing it to behave as a state in the band gap. Electrons or holes entering the localized states are therefore not available for conduction purposes and may have to acquire considerable amounts of energy to escape these states. They are therefore known astraps.
The traps may be classified by their trapping ”target”, either donors for hole traps, acceptors for electron traps or sites where the field from a hole or electron can reorientate the local structure known as a self-trap. The
”deeper” the trap, the longer a charge carrier spends in said trap, meaning deeper traps require more energy to free the charge carrier. Self-traps are a
2Due to the fact that electrons are unable to acquire energy in this region.
3Electron volts
form of space charge, meaning it causes a local field enhancement, which can be calculated using Poisson’s equation presented in equation 2.9, however with the considerations of equation 2.8 it can be expressed as such [1, 4, 6]:
∇E = ρc
ε (2.11)
where ρc is charge density, typically measured in C/m3 and ε is the permit- tivity.
2.4.2 Ionic conduction
Ionic conduction entails mass transport of charged atoms through structural defects or interfaces of a material. Ionic conduction can not operate without a steady supply of ions, which means they may either be created by elec- trolytic actions at the electrode/interface or by decomposition of the insula- tor/electrode. Ionic conduction may be divided into two sub-categories [6]:
• intrinsic conduction which proceeds by dissociation of main-chain or side groups followed by proton or/and electron transfer through hydrogen- bonded networks.
• extrinsic conduction where ions not part of the chemical structure of the material is present in the form of an impurity and permeates through the structure.
2.4.3 Electronic conduction
The process of electronic conduction has mostly been covered previously in this chapter, where the transport of electrons or holes through a band struc- ture facilitates conduction. Electrons are trapped by acceptors while holes are trapped by donors, and to leave the trap the charge need to overcome an energy potential barrier with aid from thermal/phonon excitation. A mech- anism for this charge transport can be so-called thermally activated hopping where a charge gains sufficient energy to ”hop” from one trap to the next.
Another mechanism is tunneling, where the trapped electron can not be de- fined in a particular location like particles, according to quantum mechanics.
In cases where the barrier is sufficiently narrow, the probability of the elec- tron existing on the other side of the barrier is finite, effectively tunneling through the barrier [6].
2.4.4 Schottky- and Fowler-Nordheim injection
For injection of charges from an electrode to the polymer to occur, a coulom- bic potential barrier must be overcome [1]. The charges are thermoionically excited by the applied electric field at the electrode in order to overcome the barrier with height Φ in figure 2.3 [1, 7]. The applied field affects both the height and width of the potential barrier.
Schottky injection is primarily considered in low field situations up to 109 V/m [6]. It describes how when the height of the potential barrier is reduced, the probability of electrons having sufficient energy to clear the barrier increases [1,7]. The current densityJin this instance can be expressed as such [7, 13]:
J =AT2exp(−Φ−βs√ E
kT ), where βs= s
q3 4πε0εr
(2.12) where A is the Richard-Dushman constant4, ε0 is the permittivity of free space, εr is the dielectric permittivity and E is the applied electric field.
Figure 2.3: Simplified representation of potential barrier at metal-polymer inter- face [1].
Fowler-Nordheim injection is relevant when the field is sufficiently large (> 109 V/m) as the theory for the Schottky injection mechanisms breaks down at that point [6]. It states that the width of the potential barrier at
4A= 1.2∗106Am−2K−1
this point is sufficiently thin as to facilitate electron tunneling through the barrier [1, 6].
2.5 Detection of space charges
For detection of space charges in the test objects, thePulsed Electro-Acoustic Method (PEA) is used. Even though there are other methods for space charge detection, this is the most widely used because it is cheap, simple in structure and easy to implement [14].
The working principle of the PEA method is presented schematically in figure 2.4. After a while under DC conditions, space charges will accumulate in the dielectric. The sample with thickness d is placed between two electrodes and an electrical pulse Vp(t) is applied. The electrical pulse causes slight pertur- bation from the charges and this perturbation creates an acoustic wave which propagates through the material at the speed of sound towards the detecting electrode. The acoustic signal is detected by a piezo-electric transducer and is transformed into the time-dependant electrical signal Vs(t) [14–16]:
Vs(t) = K[σ1+σ2+vsa∆T ρ(x=vsat)]ep (2.13) where σ1 and σ2 are the surface charges at the electrode, vsa is the sound velocity through the material, ∆T is the width of the pulse, ρ is the bulk charge and ep is the amplitude of the pulse voltage.
Figure 2.4: Working principle of the PEA method [15]
2.5.1 Attenuation and dispersion
Polymeric materials are generally considered as lossy, meaning acoustic waves propagating in the media will be distorted. The waves might experience attenuation and dispersion when propagating through the test object. The attenuation of a propagating acoustic pulse affects the pulse by decaying the amplitude of the pulse through the medium while also introducing a time dependent broadening of the signal [7, 17]. In figure 2.5a, an acoustic pulse with an amplitude of 1N/m2 and duration of 30 ns is applied to a non- dispersive medium with an attenuation factor of zero, while in figure 2.5b the same pulse is applied to a medium with a frequency dependent attenuation factor. In the latter case a significantly decaying amplitude can be observed while the pulse is also broadening compared to the former case [17].
(a) (b)
Figure 2.5: (a)Acoustic pulse without attenuation in the medium and(b)acoustic pulse with attenuation in the medium [17].
For dispersive media, the pulse velocity is a function of the frequency. This might mean that high frequency components of the pulse can be observed in front of- or behind the low frequency components [7, 17]. In figure 2.6a the same pulse as in figure 2.5 is applied to a medium without attenuation. In this case all frequency components propagate with the same velocity. The same pulse is applied in figure 2.6b, however the velocity of the pulse is increasing with frequency. The high-frequency components can therefore be observed in front of the waveform as these components propagate faster than the low-frequency components [17].
(a) (b)
Figure 2.6: (a) Acoustic pulse where the velocity of the pulse is not a function of the frequency and (b) acoustic pulse where the velocity of the pulse is increasing with frequency [17].
Both attenuation and dispersion will be present in any medium, meaning both factors must be accounted for when analyzing the pulses. In figure 2.7 the same pulse is applied again, but both the attenuation and the dispersion is a function of the frequency. The pulse can now be observed as significantly distorted both in amplitude and duration [17].
Figure 2.7: Acoustic wave where both attenuation and dispersion is a function of the frequency [17].
2.5.2 Calibration
To account for the aforementioned dispersion and attenuation in the material, a calibration of the system is performed. Therefore to achieve quantitative results, the factorK from equation 2.13 has to be determined. In theory, this is quite difficult to accurately calculate due to the complexity of the system.
It is therefore usually obtained experimentally [15, 17].
Calibration is performed before each test series by applying a low DC voltage over the sample. Both positive and negative polarity voltages are used to determine the factor K and the surface chargesσ1 and σ2.
3 Method
This section will present the process of making the test objects as well as the PEANUTS5 used for space charge measurements. Finally, as supplementary material an RC-equivalent circuit was made as a representation of the sample.
The test objects are made up of a .25 mm thin sheet of cross-linked DC material6 cross-linked with a .25 mm thin sheet of the same DC material.
3.1 Layered test objects
The DC material arrives in the form of pellets, meaning they have to be thermally pressed into sheets before further handling. Approximately 4.5 grams of pellets are placed in a mould consisting of an outer ring, a plate and a shim, as seen in figure 3.1.
Figure 3.1: Schematic representation of the mould
To cross-link the sample straight from pellets, they are treated in the thermal press using the program presented in table 3.1. A low pressure heating phase is required initially, while the cross-linking occurs at higher pressure and temperature.
5Pulsed ElectroAcoustic NondestrUctive Test System
6LE4253
Table 3.1: Setting of thermal press for cross-linking
- Pressure [tonnes] Temperature [°C] Time [mins]
Low pressure 3.5 120 10
High pressure 25 175 30
Water cooling 25 - 18
A different program is used for the non-cross-linked layer, presented in table 3.2. The pellets are melted at low pressure like in the previous case, however as cross-linking is not the objective, the high temperature and long high pressure phase is not required.
Table 3.2: Setting of thermal press for non-cross-linking
- Pressure [tonnes] Temperature [°C] Time [mins]
Low pressure 3.5 120 10
High pressure 25 120 2
Water cooling 25 - 10
To complete the test objects, the two layers are cross-linked together using the program presented in table 3.3. No low pressure melting is required in this case as the samples are already in the form of sheets.
Table 3.3: Setting of thermal press for layered cross-linking - Pressure [tonnes] Temperature [°C] Time [mins]
Low pressure 3.5 120 2
High pressure 25 175 30
Water cooling 25 - 18
3.1.1 Degassing
The cross-linking process produces unwanted residues which in turn may facilitate the accumulation of space charges during testing. To combat this issue, both the thin cross-linked samples and the layered samples are placed in a vacuum chamber for approximately three days at 90oC to remove as many of these impurities as possible.
3.1.2 Sputtering
An ion sputter of the type ”Jeol Fine Coat Ion Sputter JFC-1100” is used in order to achieve a well-defined electrode on the test object. The sample is
placed in a mask to hold it in place during the sputtering. Each masking plate has a hole in the middle of different sizes to correspond with the required electrode size. The side of the sample in contact with the upper electrode of the PEANUTS system requires a smaller electrode than the one in contact with the sensor electrode. For this reason, one electrode has a diameter of 7 mm while the other is 20 mm. The mask and the sample is placed in a vacuum chamber where the gold is sputtered. The vacuum is regulated in order to maintain a voltage of 1.2 kV and a current of 5 mA. The process lasts approximately 5 minutes on each side.
3.2 Experimental setup
A representation of the PEANUTS system is presented in figure 3.2, which uses the principles presented in chapter 2.5. The upper electrode is connected to a high voltage pulse generator and a high voltage amplifier, while the lower electrode (sensor electrode) is connected to an amplifier for the raw space charge signal which is further connected to the oscilloscope.
The upper electrode along with the sample is clamped to the sensor electrode and placed in a climate chamber. The chamber is used in order to regulate the temperature. The amplifier along with the oscilloscope and the other high voltage equipment are located outside of the chamber.
Figure 3.2: Representation of the PEANUTS measurement setup. [18]
A custom program is written in order to execute measurements at the desired intervals. There is a higher concentration of measurements at the beginning of the program, however the number of measurements are reduced after one day has passed. A series typically lasts for one week before the sample is replaced and a new series begins.
The custom program is written to take bothvoltage-on-andvoltage-off mea- surements. Thevoltage-onmeasurements are useful when reviewing the over-
all field distribution, including both momentary- and trapped charges, while the voltage-off measurements are useful when reviewing only the trapped charges. In combination they give a complete view of how the charges are trapped throughout the sample and how they affect the overall field while voltage is applied.
To ensure the experimental setup is working properly, a dummy test object is used in combination with a shortened measurement program before any of the proper test series are initiated. By doing this, the execution of the measurement program can be evaluated without waiting for an entire series to finish. In addition, the high voltage- and ground- acoustic matching sheets are replaced on the brass electrode before any test series are initiated to ensure the signal is as good as possible.
3.2.1 Conditioning
Before any new measurement series, the upper brass electrode and the sam- ple are conditioned at the new temperature for approximately one day in order to account for thermal expansion. If the electrode and sample are clamped together before expansion, it might cause an inadequate pressure over the sample which might affect the results. The subjects are therefore placed separately inside the climate chamber. After the conditioning period, the subjects are mounted on the setup and prepared for a second, shorter conditioning period before calibration.
3.2.2 Calibration
As previously stated in chapter 2.5.2, proper calibration of the sample is required for qualitative analysis. A custom program is written in order to record calibration measurements for the samples. Low DC voltages with both positive and negative polarities are applied to the sample for one minute at a time. Voltages of 1, 2 and 3 kV are applied. After calibration, a short discharge period of the sample is executed in order to reduce the charges trapped during calibration.
3.3 RC-equivalent circuit
As the charge accumulation (and as a result, the field distribution) varies significantly throughout the sample, the equivalent circuit is divided into several sections to better represent the different field distortions in a partic- ular region of the sample. Figure 3.3 displays how the sample is divided into the different sections based on the field distortion. A detailed description of
the calculated conductivities as well as the values of the RC-components can be found in Appendix A.1.
R1
C1
R2
C2
R3
C3
R4
C4
R5
C5
R6
C6
Figure 3.3: RC-equivalent circuit divided into appropriate sections.
As the sections are divided appropriately as to encapsulate the charge accu- mulation in the particular region, the sections are of different thicknesses. A detailed description of the different sections and their corresponding equiva- lent components as well as the thickness of the section is presented in table 3.4.
Table 3.4: Description of the different sections and their corresponding equivalent components.
Section Equivalent components Percentage of sample
Cathode R1, C1 10.5
Cathode-bulk R2, C2 26.9
Cathode-interface R3, C3 9
Anode-interface R4, C4 11.1
Anode-bulk R5, C5 29
Anode R6, C6 13.5
The capacitances are calculated using the geometry of the sample. In par- ticular, the equation for parallel plate capacitors is used:
C =εrε0
A
d (3.1)
where εr is the relative permittivity of the sample andε0 is the permittivity of free space. The resistance values are approximated under the assumption that the current densities are constant between the sections at steady-state.
Equation 2.1 can be modified under this assumption to find the ratio of the conductivities between the sections:
σ1
σ2 = EDC+E2
EDC+E1 (3.2)
whereσn is the conductivity of a particular section andEnis the field due to space charges of the same section. The reference conductivity of the single cross-linked layer was previously measured in [19].
4 Results
This section will present both the results of the conducted space charge measurements, as well as the modeling of the resulting field distribution using the RC-equivalent. For the measurements, both the results of the voltage-on andvoltage-off are presented to distinguish between fast and slow charges. Within these categories, both the charge- and field-distributions are presented. A detailed description of the different measurement series are presented in table 4.1. A final series at 80°C was planned, but due to failing equipment it was not completed. The equivalent RC circuits were designed and simulated using Simulink and compared with the measured results.
Table 4.1: Detailed description of the measurement series.
Test object L1 L2 L3
Estimated thickness [mm] 0.5 0.5 0.5 Actual thickness [mm] 0.45 0.45 0.45 Applied DC voltage [kV] 10 10 10
Temperature [°C] 20 40 60
4.1 Layered test objects
4.1.1 L1 - 20 kV/mm - 20°C
This section will present the results of the test series carried out on a layered test object at an ambient temperature of 20°C. The applied voltage is 10 kV giving an average field over the sample of 22.2 kV/mm. As of the 5th day of the series, an issue occurred with the scaling of the oscilloscope leading to an inconsistency in the measurements of the charge distribution thereafter.
Even though the values of both charges and field at that point are unreliable7 they are included in the figures anyway as they still show a clear trend for the development of charges.
7Measures have been taken in order to make these results as cohesive as possible, however the discrepancy is still noticeable, particularly in the voltage-on measurements.
Figure 4.1: Space charge distribution over the layered test object at 20°C for 7 days based on voltage-off measurements. Interface between cross-linked and double cross-linked materials is marked with dotted line.
From figure 4.1 there can be observed homocharge build-up at both elec- trodes after 10 minutes, while at the internal interface minuscule amounts of positive and negative charges build up at the cathode- and anode-side respec- tively. After approximately 1 day, the net charges at the cathode switches to heterocharges. At the anode the homocharges reaches an apex after approx- imately 3 hours where it remains relatively stable until 1 day when the net charge accumulation dwindles until 5 days when it starts to increase once again. At the internal interface negative charges builds up quite quickly and continues to increase throughout the series. There is no sign of a slowdown of charge accumulation after 7 days which indicates that a steady-state has not been reached.
Figure 4.2 displays how the slow charges impact the overall charge distri- bution of the sample. At the cathode the accumulation of heterocharges are signified by the declining apex of the electrode. A leap can be observed between day 4 and 5 signifying the change in oscilloscope setting, however even after the discrepancy, changes can still be observed meaning no steady- state is reached. At the anode the net charge accumulation is quite constant throughout the series, which can be confirmed using figure 4.1 where the development of the charge magnitude at the anode is insignificant compared to the momentary charges. At the interface a gradual build-up of negative
charges can be observed which matches the measurements in figure 4.1.
Figure 4.2: Charge distribution over the layered test object at 20°C for 7 days based on voltage-on measurements. Interface between cross-linked and double cross-linked materials is marked with dotted line.
Corresponding field
The development of the electric field due to space charges are presented in figure 4.3 while the total field, including both momentary and slow charges are presented in figure 4.4. At the initiation of the series there is a weak negative field enhancement across the entire sample, but as the increase in net heterocharges develops at the cathode the single cross-linked layer experience a field enhancement of opposite polarity as the applied voltage, seen further in figure 4.4. The negative charges at the interface gives a positive field enhancing effect on the double cross-linked layer.
Using equation 2.10 the maximum local field enhancement at the anode is 6.7%, while the local field reduction at the cathode is 9.1%8.
8Values taken after 4 days due to the aforementioned oscilloscope error.
Figure 4.3: Development of electric field over the layered test object at 20°C for 7 days based on voltage-off measurements. Interface between cross-linked and double cross-linked materials is marked with dotted line.
Figure 4.4: Development of electric field over the layered test object at 20°C for 7 days based onvoltage-on measurements. Interface between cross-linked and double cross-linked materials is marked with dotted line.
4.1.2 L2 - 20 kV/mm - 40°C
This section will present the results of the test series carried out on a layered test object at an ambient temperature of 40°C. The applied voltage is 10 kV giving an average field over the sample of 22.2 kV/mm.
Figure 4.5: Space charge distribution over the layered test object at 40°C for 7 days based on voltage-off measurements. Interface between cross-linked and double cross-linked layers is marked with dotted line.
Figure 4.5 shows how a small amount of heterocharges builds up close to the cathode while homocharges of similar amplitude builds up at the anode after a short time. It is worth noting that no significant amount of homocharges can be observed at any point at the cathode. Throughout the series, the heterocharges at the cathode keeps increasing and does not seem to reach steady-state after 7 days, but the accumulation has significantly slowed down at that point. At the anode the homocharges keep increasing in magnitude throughout the series, but not at the same rate as the accumulation at the cathode. At the internal interface, negative charges appear to accumulate at the single cross-linked side with an increasing amplitude throughout the series. At the double cross-linked side, positive charges appear to accumulate, but the amplitude peaks after approximately 1 day, after which it decays for the remainder of the series.
In figure 4.6 the effect of the development of the space charges can be seen on the overall charge distribution. The cathode experience a significant ampli-
tude decay throughout the series, while the anode experience an increase in its amplitude. The negative and positive charges at each side of the interface can also be observed.
Figure 4.6: Charge distribution over the layered test object at 40°C for 7 days based on voltage-on measurements. Interface between cross-linked and double cross-linked materials is marked with dotted line.
Corresponding field
The development of the electric field due to space charges are presented in figure 4.7 while the total field, including both momentary and slow charges are presented in figure 4.8. Throughout the length of the series, the cath- ode side (single cross-linked layer) experiences a negative field enhancement, continuously increasing in amplitude. Oppositely, the anode side (double cross-linked layer) experiences a positive field enhancement throughout the series. No apparent steady-state is achieved at the end of the 7 days.
Using equation 2.10 the maximum field enhancement at the anode is 40.4%, while the field reduction at the cathode is 47.4%.
Figure 4.7: Development of electric field over the layered test object at 40°C for 7 days based on voltage-off measurements. Interface between cross-linked and double cross-linked materials is marked with dotted line.
Figure 4.8: Development of electric field over the layered test object at 40°C for 7 days based onvoltage-on measurements. Interface between cross-linked and double cross-linked materials is marked with dotted line.
4.1.3 L3 - 20 kV/mm - 60°C
This section will present the results from the test series carried out on a layered test object at an ambient temperature of 60°C. The applied voltage is 10 kV giving an average field over the sample of 22.2 kV/mm.
Figure 4.9: Space charge distribution over the layered test object at 60°C for 7 days based on voltage-off measurements. Interface between cross-linked and double cross-linked materials is marked with dotted line.
From figure 4.9 it can be observed that a large amount of homocharges build up at the cathode at the beginning of the series. In addition, a similarly large amount of heterocharges build up in the region adjacent to the cathode.
Some homocharges can be observed at the anode at the beginning of the series which peaks in amplitude after approximately 1 hour. At the internal interface, some charge build-up can also be recorded at the beginning of the series. Throughout the series the amplitude of the net charges at the cathode decays and after 7 days there is limited development as it reaches a somewhat stable amount of heterocharges. The homocharges at the cathode also decays in amplitude up to 7 days and is relatively stable at this point. Migration of charge peaks in and around the internal interfaces occur throughout the length of the series, but remains relatively stable at the 7 day mark with negative charge build-up at the single cross-linked layer and positive charge build-up at the double cross-linked layer.
The total charge development, including both momentary and slow charges can be viewed in figure 4.10. The peak amplitude at the cathode can be observed after 1 hour, after which it decays throughout the series. The anode experiences a local peak at the initiation of the series and decays in amplitude up to about 12 hours before the amplitude increases until the end of the series. The migration of the charge peaks at the internal interface can be detected, which corresponds with the observations from the voltage-off measurements.
Figure 4.10: Charge distribution over the layered test object at 60°C for 7 days based on voltage-on measurements. Interface between cross-linked and double cross-linked layer is marked with dotted line.
Corresponding field
The development of the electric field due to space charges are presented in figure 4.11 while the total field, including both momentary and slow charges are presented in figure 4.12. The accumulation of homocharges at the cath- ode during the beginning of the series contribute to a local positive field enhancement which turns into a negative field enhancement when the net homocharges develop into net heterocharges. At the anode there is a pos- itive field enhancement after 1 hour, corresponding with the observations from figure 4.9. After this the enhancement decreases until approximately 12 hours before it increases until the end of the series. At the internal in- terface the field keeps increasing in amplitude throughout the length of the series.
Using equation 2.10 the maximum field enhancement at the anode is 8%, while the local field reduction at the cathode is 16.8%.
Figure 4.11: Development of electric field over the layered test object at 60°C for 7 days based on voltage-off measurements. Interface between cross-linked and double cross-linked materials is marked with dotted line.
Figure 4.12: Development of electric field over the layered test object at 60°C for 7 days based on voltage-on measurements. Interface between cross-linked and double cross-linked materials is marked with dotted line.
4.2 The temperature effect
This section will review the effect the temperature has on the development of the electric field in the samples.
0 1 2 3 4 5 6 7
days -10
-8 -6 -4 -2 0 2
Ex(kV/mm)
Section 1 field development
20°C measured 40°C measured 60°C measured 20°C RC model 40°C RC model 60°C RC model
0 1 2 3 4 5 6 7
days -8
-7 -6 -5 -4 -3 -2 -1 0 1
Ex(kV/mm)
Section 2 field development
20°C measured 40°C measured 60°C measured 20°C RC model 40°C RC model 60°C RC model
0 1 2 3 4 5 6 7
days -2.5
-2 -1.5 -1 -0.5 0 0.5 1
Ex(kV/mm)
Section 3 field development
20°C measured 40°C measured 60°C measured 20°C RC model 40°C RC model 60°C RC model
0 1 2 3 4 5 6 7
days -1.5
-1 -0.5 0 0.5 1 1.5 2 2.5
Ex(kV/mm)
Section 4 field development
20°C measured 40°C measured 60°C measured 20°C RC model 40°C RC model 60°C RC model
0 1 2 3 4 5 6 7
days -1
0 1 2 3 4 5 6
Ex(kV/mm)
Section 5 field development
20°C measured 40°C measured 60°C measured 20°C RC model 40°C RC model 60°C RC model
0 1 2 3 4 5 6 7
days -2
0 2 4 6 8 10
Ex(kV/mm)
Section 6 field development
20°C measured 40°C measured 60°C measured 20°C RC model 40°C RC model 60°C RC model
Figure 4.13: Development of electric field due to space charges over time for the different sections of the samples. Results according to the different equivalent RC-circuits are also included.
Figure 4.13 presents the development of the electric field for the different sections of the samples over time. The sections are divided according to table 3.4. It can be observed that the magnitude of the field enhancement is typically greater at 40°C than at other temperatures, while the magnitudes at 20 & 60 °C are approximately the same in value. The exception to this is at the interface sections where all magnitudes are quite similar compared to the other sections. The distribution of all the samples can be related to a Maxwell capacitor, presented by Kreuger in [20]. This generally means that one layer will experience a time-dependent field reduction, while the other will experience a time-dependent field enhancement. While it is not illustrated in figure 4.13, the theory for a Maxwell capacitor also states there will be a time-dependent accumulation of charges at the interface which can be seen in figures 4.1, 4.5 and 4.9.
The development at 20 °C suggests the field follows the charge of a typi- cal capacitor where the charging time is dominated by a time constant τ (demonstrated in [4]). Initially, the field distribution is dominated by the permittivity of the layers, which means there is a capacitive field distribu- tion dictated by the geometry of the sample. Slowly, the field over the sam- ple redistributes into one dominated by the conductivity of the dielectrics, meaning the trend is towards a resistive field distribution. Over time, a quasi steady-state should be reached, however the length of the measurement series does not allow any conclusion to be drawn regarding this matter. It is also worth noting that the same precautions apply for the results of the 20 °C here as previously mentioned, where the results after 4 days are considered unreliable, but are still included to show a general trend.
At 40°C additional mechanisms can be observed compared to the 20°C case.
At both interface sections as well as the double cross-linked bulk section different accumulation rates can be observed during the first 24 hours of the series. Local peaks generally forms within the first 12 hours before the accumulation reverses for the rest of the series. At the interface of the double cross-linked layer the accumulation also has a second local peak after 24 hours before the accumulation once again reverses.
At 60 °C there are also additional mechanisms compared to the 20 °C case, however not necessarily the same as for the 40 °C case. Particularly at the interface sections a large impulse can be observed up to one hour before the field gradually reaches a quasi steady-state. Similar phenomena can also be observed at the other sections, except for the cathode section, however with a lower peak amplitude.
4.3 RC-equivalent
This section will present the results of the simulations carried out on the RC-equivalent circuit and compare them with the results of the PEANUTS measurements. Results are presented in figure 4.13. As previously stated: the reference conductivity of the single cross-linked layer used for the resistance values is based on measurements performed by Hagen in [19], however it was quite clear that these values would not suffice as the time constant τ of the field development would be way lower than the one observed from the measurements. Previous research on the DC conductivity of XLPE (see ref. [21–24]) suggest large fluctuations in this particular property. Combining these two factors lead to the decision of reducing the calculated value of the different conductivities by a factor of 5 (and in turn increasing the resistance value by a factor of 5) to better fit the curves of the measurements.
The model generally predicts the field development in the different sections correctly, however the magnitude of the enhancement can be slightly off. As the model is highly simplified, it fails to predict the mechanisms occurring early in measurements at higher temperatures. As the field development at 20 °C does not show signs of complicated mechanisms, the model fits well with this series.
As the measured time constant appears to vary slightly throughout the sam- ple, the model typically fails to predict the development rate of the field.
In some cases, like at the cathode and anode-interface at 20 °C, the model fits quite well with the measurements, while in other cases, like the anode- interface and anode-bulk at 40 °C, the model would need significant adjust- ments to fit the measurements.
5 Discussion
The accumulation of space charges in layered polymeric DC insulation has been investigated alongside the effect temperature has on this phenomenon.
All samples are constructed using a layer of XLPE which in turn is cross- linked with a layer of non-cross-linked polyethylene. The PEA method is used to conduct the measurements. Finally, the viability of using an equivalent RC circuit to simulate the field development has been evaluated. This section will investigate the mechanisms for the acquired results.
5.1 Charge development
Electrode-polymer interface
Regarding the electrode-polymer interfaces, slightly different observations can be made for the different temperatures. At 20°C (fig. 4.1) homocharges can be observed at both electrodes early in the series. Over time the net charges at the cathode develops into heterocharges, and after 1 day no ho- mocharges can be observed. The homocharges observed at the anode remain throughout the series, however fluctuating in amplitude. At 40°C (fig. 4.5) homocharges are observed at the anode, however the net charges at the cath- ode indicate a presence of heterocharges throughout the entire series. At 60°C (fig. 4.9) a significant amount of homocharges are observed early in the series at the cathode with mirrored charges in the adjacent region. Similarly, ho- mocharges can be observed at the anode, although with a lower amplitude, and mirrored charges can be observed at the adjacent region. Within one day, the homocharges at the cathode as well as the mirrored charges amalga- mates into net heterocharges with a lower amplitude than what both regions initially had. The same phenomenon can also be observed at the anode where the homocharges and its mirrored charges form net homocharges over time.
As per theory presented previously in this thesis (see chapter 2.3.1) the devel- opment of homocharges at the electrode means charge injection occur faster than the dielectric is capable of transporting the charges, while the hete- rocharge development means the transport occur faster than the injection.
The charge injection has been reported to be temperature dependent [25].
The charge injection is also dependent upon several other factors such as the electrode material, dielectric material and residual by-products in the dielectric where any of these factors may also be temperature dependent or vary from sample to sample [9, 26, 27]. Combining all these factors make the charge injection difficult to quantify and attributing the space charge formation to the varying charge injection may be difficult.
However, what can be seen from the measured results is that typically the injection of positive charges at the anode is greater than the transport regard- less of the temperature. On the contrary, the transport of positive charges to the cathode will eventually be greater than the injection of negative ones for all temperatures. The reason for the charge polarity switch at the cathode over time has previously been presented by Hagen [19] and may be attributed to electronic transport occurring faster than ionic transport, leading to elec- tronic transport being dominant early in the series while ionic transport slowly becoming more dominant as time passes. Another theory is that dif- ferent charges have different mobility in the different layers. The theory has previously been presented by Rogti & Ferhat [26] and might mean that posi- tive injected charges at the anode move slower towards the cathode than the negative injected charges at the cathode move in the opposite direction. The dielectric interface may also affect this, but this will be discussed later. The heterocharge scheme which arises is unlikely to be due to the ionization of cross-linking by-products as the samples have been thoroughly treated after cross-linking, meaning the heterocharges are more likely to be attributed to blocking capabilities of the electrode-insulation interface [9]. What remains uncertain is why no homocharge at the cathode at 40°C can be observed at any point.
Dielectric interface
In all series, charges of opposite polarity as the applied voltage accumulate at the dielectric interface. At 40°C negative charges accumulate at the cath- ode side of the interface with positive charges accumulating at the anode side of the interface, although with a much lower amplitude compared to the negative charges. At 60°C negative and positive charges accumulate at the cathode- and anode-side, respectively, but this time with quite similar amplitudes. The greatest accumulation occurs at 40°C, while the amount of charges are quite similar at 20 and 60°C, so the accumulation does not necessarily increase with increasing temperature.
The theory of Maxwell-Wagner (MW) polarization (see chapter 2.3.2) states that a discontinuity in the conductivity or permittivity of layered specimen may facilitate charge build-up at the interface. Another reason for the inter- facial charge build-up has been attributed to the electrode material [26]. If the interfacial charges are mainly due to MW polarization one would expect the two materials to be most dissimilar at 40°C as this is where the most charge build-up occurs. Further investigation into this matter would be of interest going forward.
At lower temperatures negative charges are the main cause for charge accu-
mulation at the dielectric interface. The trend shifts with increasing temper- ature, as positive charges can be observed at the anode side of the interface and at 60°C the amplitude of the charges at each side of the interface are quite similar. The effect the interface has on charge accumulation has previ- ously been studied by Chen et al. [28] and the interface has been found to be more prone to blocking negative charges than positive ones. When the tem- perature is increased, an increasing amount of positive charges are blocked at the interface, while more negative charges are blocked at 40°C than 20°C, but drops off drastically when the temperature is increased further to 60°C.
It may indicate that negative charges are more capable of transport between the layers at higher temperatures. On the contrary, the transport of positive charges appear to decrease between the layers with increasing temperature.
As the PEA system measures net charges, the apparent increase in trapped positive charges at higher temperatures may rather be attributed to a deple- tion of negative charges at the interface.
Overall charge development
As previously presented, the greatest charge accumulation occurs at 40°C, while the accumulation at 20 & 60°C are quite similar. These results confirm that several mechanisms are contributing to the overall charge development.
From research by Bodega [9] the charge accumulation is expected to keep increasing in the temperature range of 20-60°C, which it does not. A possi- ble explanation of this comes from Lan et al. [25] as their research indicated that the space charge formation rate increases slower than the charge de- trapping rate as a function of the temperature. What this would entail is an increase in the accumulated charges with increasing temperature up to a certain point where the accumulation would begin decreasing. The mobility of charge carriers has also been observed to increase significantly with in- creasing temperature, possibly affecting the charge trapping and detrapping rate as well as the conduction. This theory fits well with what has been observed in this project.
The morphology may also affect the acquired results. Differential Scanning Calorimetry (DSC) measurements were performed on one of the layered sam- ples and compared with a sample of XLPE, which are presented in appendix A.2 alongside a short explanation of the procedure. The XLPE sample had a degree of crystallinity of 27.9%, while the first layered sample had 33.4% and the second had 31.8%, meaning the double cross-linking process increased the degree of crystallinity. Increasing the degree of crystallinity will in turn reduce the amorphous regions of the sample. Amorphous regions, as well as the interfacial regions between amorphous and crystalline regions have
